Forecasting exchange rates using general regression neural networks

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<ul><li><p>Computers &amp; Operations Research 27 (2000) 1093}1110</p><p>Forecasting exchange rates using general regression neuralnetworks</p><p>Mark T. Leung!,*, An-Sing Chen", Hazem Daouk#</p><p>!Division of Management and Marketing, College of Business, University of Texas at San Antonio,San Antonio, TX 78249, USA</p><p>"Department of Finance, National Chung Cheng University, Ming Hsiung, Chia Yi 612, Taiwan, ROC#Department of Finance, Kelley School of Business, Indiana University, Bloomington, IN 47405, USA</p><p>Abstract</p><p>In this study, we examine the forecastability of a speci"c neural network architecture called generalregression neural network (GRNN) and compare its performance with a variety of forecasting techniques,including multi-layered feedforward network (MLFN), multivariate transfer function, and random walkmodels. The comparison with MLFN provides a measure of GRNNs performance relative to the moreconventional type of neural networks while the comparison with transfer function models examines the di!erencein predictive strength between the non-parametric and parametric techniques. The di$cult to beat random walkmodel is used for benchmark comparison. Our "ndings show that GRNN not only has a higher degree offorecasting accuracy but also performs statistically better than other evaluated models for di!erent currencies.</p><p>Scope and purpose</p><p>Predicting currency movements has always been a problematic task as most conventional econometricmodels are not able to forecast exchange rates with signi"cantly higher accuracy than a naive random walkmodel. For large multinational "rms which conduct substantial currency transfers in the course of business,being able to accurately forecast the movements of exchange rates can result in considerable improvement inthe overall pro"tability of the "rm. In this study, we apply the general regression neural network (GRNN) topredict the monthly exchange rates of three currencies, British pound, Canadian dollar, and Japanese yen.Our empirical experiment shows that the performance of GRNN is better than other neural network andeconometric techniques included in this study. The results demonstrate the predictive strength of GRNN andits potential for solving "nancial forecasting problems. ( 2000 Elsevier Science Ltd. All rights reserved.</p><p>Keywords: General regression neural networks; Currency exchange rate; Forecasting</p><p>*Corresponding author. Tel.: #1-210-458-5776; fax: #1-210-458-5783.E-mail addresses: (M.T. Leung), " (A.-S. Chen),</p><p>(H. Daouk)</p><p>0305-0548/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 3 0 5 - 0 5 4 8 ( 9 9 ) 0 0 1 4 4 - 6</p></li><li><p>1. Introduction</p><p>Applying quantitative methods for forecasting in "nancial markets and assisting investmentdecision making has become more indispensable in business practices than ever before. For largemultinational "rms which conduct substantial currency transfers in the course of business, beingable to accurately forecast movements of currency exchange rates can result in substantialimprovement in the overall pro"tability of the "rm. Nevertheless, predicting exchange ratemovements is still a problematic task. Most conventional econometric models are not able toforecast exchange rates with signi"cantly higher accuracy than a naive random walk model. Inrecent years, there has been a growing interest to adopt the state-of-the-art arti"cial intelligencetechnologies to solve the problem. One stream of these advanced techniques focuses on the use ofarti"cial neural networks (ANN) to analyze the historical data and provide predictions to futuremovements in the foreign exchange market. In this study, we apply a special class of neuralnetworks, called general regression neural network (GRNN), to forecast the monthly exchangerates for three internationally traded currencies, Canadian dollar, Japanese yen, and British pound.In order to provide a fair and robust evaluation of the GRNN, relative performance against otherforecasting approaches are included in our empirical investigation. Speci"cally, the performance ofthe GRNN is compared with those of the multi-layered feedforward neural network (MLFN), thetype of ANN used in many research studies, and the models based on multivariate transferfunction, a general econometric forecasting tool. In addition, random walk forecasts are generatedto give benchmark comparisons.</p><p>The remainder of this paper is organized as follows. A review of the literature is given in the nextsection. In Section 3, we give an explanation of the logic and operations used by the GRNN. Then,a description of the empirical data employed in our study is provided in Section 4. This section alsoexplains the neural network training paradigm and presents the model speci"cations for theforecasting approaches tested in the experiment. In Section 5, a description to our statistical analysesis presented and the experimental "ndings are discussed. The paper is then concluded in Section 6.</p><p>2. Literature review</p><p>2.1. Exchange rate forecasting</p><p>The theory of exchange rate determination is in an unsatisfactory state. From the theoreticalpoint of view, the debates between the traditional #ow approach and the modern asset-marketapproach have seen the victory of the latter. However, from the empirical point of view, theforecasting ability of the theoretical models remains very poor. The results of Meese and Rogo![1}3] came as a shock to the profession. According to these studies, the current structural modelsof exchange-rate determination failed to outperform the random walk model in out-of-sampleforecasting experiments even when the actual realized values of the explanatory variables were used(ex-post forecasts). The results of Meese and Rogo! have been con"rmed in many subsequentpapers (e.g., Alexander and Thomas [4], Gandolfo et al. [5,6], and Sarantis and Stewart, [7,8]).Moreover, even with the use of sophisticated techniques, such as time-varying-coe$cients, theforecasts are only marginally better that the random walk model [9].</p><p>1094 M.T. Leung et al. / Computers &amp; Operations Research 27 (2000) 1093}1110</p></li><li><p>The models considered by Meese and Rogo! were the #exible-price (Frenkel}Bilson) monetarymodel, the sticky-price (Dornbusch}Frankel) monetary model, and the sticky-price (Hooper}Morton) asset model. Other models for exchange rate forecasting include the portfolio balancemodel, and the uncovered interest parity model. Of the three models used by Meese and Rogo!, theHooper}Morton model is more general and nests the other two models. However, as argued in theprevious paragraph, those three models have been shown to be unsatisfactory. The evidence relatedto the portfolio balance model was ambiguous [7]. On the other hand, both Fisher et al. [10] andSarantis and Stewart [7] found that the models based on a modi"ed uncovered interest parity(MUIP) approach showed some promising results compared to the other conventional theoreticalapproaches. In a related paper, Sarantis and Stewart [8] provided evidence that exchange rateforecasting models based on the MUIP produced more accurate out-of-sample forecasts than theportfolio balance model for all forecast horizons, thus arguing in favor of the MUIP approach toexchange rate determination and forecasting.</p><p>In light of the previous literature, we will consider both univariate and multivariate approachesto exchange rate forecasting. Furthermore, given the mounting evidence favoring the MUIPapproach to exchange rate modeling, we use the MUIP relationship as the theoretical basis for ourmultivariate speci"cations in our experimental investigation.</p><p>2.2. MUIP exchange rate relationship</p><p>Essentially, Sarantis and Stewart [7,8] showed that the MUIP relationship can be modeled andwritten as follows:</p><p>et"a</p><p>0#a</p><p>1(rHt!r</p><p>t)#a</p><p>2(nH</p><p>t!n</p><p>t)#a</p><p>3(pH</p><p>t!p</p><p>t)#a</p><p>4(ca</p><p>t/ny</p><p>t)#a</p><p>5(caH</p><p>t/nyH</p><p>t)#k</p><p>t, (1)</p><p>where e is the natural logarithm of the exchange rate, de"ned as the foreign currency price ofdomestic currency. r,n, p, and (ca/ny) represent the logarithm of nominal short-term interest rate,expected price in#ation rate, the logarithm of the price level, and the ratio of current account tonominal GDP for the domestic economy, respectively. Asterisks denote the corresponding foreignvariables. k is the error term. The variables (ca/ny) and (caH/nyH) are proxies for the risk premium.Eq. (1) is a modi"ed version of the real uncovered interest parity (MUIP) relationship adjusted forrisk. Sarantis and Stewart [7] provided a more detailed discussion and investigation of thisrelationship.</p><p>2.3. Applications of neural networks</p><p>In the last decade, applications associated with arti"cial neural network (ANN) has been gainingpopularity in both the academic research and practitioners sectors. The basic structure of andoperations performed by the ANN emulate those found in a biological neural system. Basic notionsof the concepts and principals of the ANN systems and their training procedures can be found inRumelhart and McClelland [11], Lippman [12], and Medsker et al. [13]. Many of the countlessapplications of this arti"cial intelligence technology are related to the "nancial decision making.Hawley et al. [14] provide an overview of the neural network models in the "eld of "nance.</p><p>According to Hawley et al., there is a diversity of "nancial applications for neural networks in theareas of corporate "nance, investment analysis, and banking. A review on recent literature also</p><p>M.T. Leung et al. / Computers &amp; Operations Research 27 (2000) 1093}1110 1095</p></li><li><p>reveals "nancial studies on a wide variety of subjects such as bankruptcy prediction [15,16],prediction of savings and loan association failures [17], credit evaluation [18,19], analysis of"nancial statements [20], corporate distress diagnosis [21], bond rating [22], initial stock pricing[23], currency exchange rate forecasting [24], stock market analysis [25}27], and forecasting infutures market [28,29].</p><p>2.4. Studies using general regression neural networks</p><p>GRNN is a class of neural networks which is capable of performing kernel regression and othernon-parametric functional approximations. Although GRNN has been shown to be a competenttool for solving many scienti"c and engineering problems (e.g., signal processing [30]), chemicalprocessing [31], structural analysis [32], assessment of high power systems [33], the technique hasnot been widely applied to the "eld of "nance and investment. The only one "nancial studyprimarily based on GRNN is Wittkemper and Steiner [34] in which the regression network is usedto verify the predictability of the systematic risk of stocks.</p><p>3. General regression neural network</p><p>The general regression neural network (GRNN) was originally proposed and developed bySpecht [35]. This class of network paradigm has the distinctive features of learning swiftly, workingwith simple and straightforward training algorithm, and being discriminative against infrequentoutliers and erroneous observations. As its name implies, GRNN is capable of approximating anyarbitrary function from historical data. The foundation of GRNN operation is essentially based onthe theory of nonlinear (kernel) regression* estimation of the expected value of output given a setof inputs. Although GRNN can provide a multivariate vector of outputs, without loss of generality,our description of the GRNN operating logic is simpli"ed to the case of univariate output. Eq. (2)summarizes the GRNN logic in an equivalent nonlinear regression formula:</p><p>E[yDX]":=~=yf (X, y) dy:=~=</p><p>f (X, y) dy, (2)</p><p>where y is the output predicted by GRNN, X the input vector (x1, x</p><p>2,2, xn ) which consists of</p><p>n predictor variables, E[yDX] the expected value of the output y given an input vector X, and f (X, y)the joint probability density function of X and y.</p><p>3.1. Topology of GRNN</p><p>The topology of GRNN developed by Specht [35] primarily consists of four layers of processingunits (i.e., neurons). Each layer of processing units is assigned with a speci"c computationalfunction when nonlinear regression is performed. The "rst layer of processing units, termed inputneurons, are responsible for reception of information. There is a unique input neuron for eachpredictor variable in the input vector X. No processing of data is conducted at the input neurons.The input neurons then present the data to the second layer of processing units called pattern</p><p>1096 M.T. Leung et al. / Computers &amp; Operations Research 27 (2000) 1093}1110</p></li><li><p>neurons. A pattern neuron is used to combine and process the data in a systematic fashion suchthat the relationship between the input and the proper response is memorizeda. Hence, thenumber of pattern neurons is equal to the number of cases in the training set. A typical patternneuron i obtains the data from the input neurons and computes an output h</p><p>iusing the transfer</p><p>function of</p><p>hi"e~(X~Ui ){(X~Ui )@2p2, (3)</p><p>where X is the input vector of predictor variables to GRNN, ;i</p><p>is the speci"c training vectorrepresented by pattern neuron i, and p is the smoothing parameter.</p><p>Eq. (3) is the multivariate Gaussian function extended by Cacoullos [36] and adopted by Spechtin his GRNN design.</p><p>The outputs of the pattern neurons are then forwarded to the third layer of processing units,summation neurons, where the outputs from all pattern neurons are augmented. Technically, thereare two types of summations, simple arithmetic summations and weighted summations, performedin the summation neurons. In GRNN topology, there are separate processing units to carry out thesimple arithmetic summations and the weighted summations. Eqs. (4a) and (4b) express themathematical operations performed by the &amp;simple summation neuron and the &amp;weighted summa-tion neuron, respectively.</p><p>S4"+</p><p>i</p><p>hi, (4a)</p><p>S8"+</p><p>i</p><p>wihi. (4b)</p><p>The sums calculated by the summation neurons are subsequently sent to the fourth layer ofprocessing unit, the output neuron. The output neuron then performs the following division toobtain the GRNN regression output y:</p><p>y"S8S4</p><p>. (5)</p><p>Fig. 1 illustrates the schematic sketch of the GRNN design and its operational logic describedabove. It should be noted that the depicted network construct is valid for any model withmultivariate outputs. The speci"c design for exchange rate forecasting in our study has only one(univariate) output neuron.</p><p>4. Exchange rate forecasting</p><p>4.1. Data</p><p>The sample data applied to this study are collected from the AREMOS data base maintained bythe Department of Education of Taiwan. The entire data set covers 259 monthly periods runningfrom January 1974 through July 1995. To serve di!erent purposes, the data are divided into threesets: the training set (129 months from January 1974 through September 1984), the model</p><p>M.T. Leung et al. / Computers &amp; Operations Research 27 (2000) 1093}1110 1097</p></li><li><p>Fig. 1. General GRNN construct. A typical GRNN construct consists of four layers } of processing units } input,pattern, summation, and output neurons. Input layer receives the input vector X and distributes the...</p></li></ul>


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